Canadian Fernandez, the 2021 US Open runner-up, was playing only her third singles match since returning from a foot injury she suffered at the French Open.
The 19-year-old lefthander, who lost to fellow teenager Emma Raducanu in last year's Flushing Meadows final, led 3-0 in the first set and 5-1 in the second but could not press home her advantage, allowing world number 27 Alexandrova to rally and take the match in straight sets.
Unseeded American Amanda Anisimova improved her head-to-head record against ninth seed Daria Kasatkina to 3-0 with a 6-4 6-4 win over the Russian.
The 20-year-old Wimbledon quarter-finalist peppered the court with 33 winners to five from Kasatkina, who fell to a second straight loss since winning in San Jose.
Cincinnati-born Caty McNally (20) also secured victory, overcoming leg cramps to beat Aliaksandra Sasnovich 6-3 3-6 7-6(2). McNally grabbed at her left leg in pain after her first serve on match point and it briefly looked like she might not be able to finish.
However, she played through the pain and collapsed on her back after securing victory, with Belarusian Sasnovich then walking around the net to McNally's side to embrace her.
"At the end it was just a little bit of relief of fighting through that," McNally, ranked 179th in the world, told reporters after setting up a second-round clash against twice Wimbledon champion Petra Kvitova.
"There was definitely a lot of pain and some cramping going on, so it was just such a mental battle.
"I was just so proud of myself fighting through that when I think I could have just thrown in the towel there and blame it on not having my legs with me."
Rybakina had a relatively comfortable outing against Egyptian Mayar Sherif, winning 6-3 6-2, but both Kvitova and Victoria Azarenka were forced to dig deep.
Kvitova saved a match point to beat last year's runner-up Jil Teichmann 6-7(2) 7-6(6) 6-3 while two-time Australian Open winner Azarenka defeated Kaia Kanepi 6-3 4-6 6-3.
Azarenka will next meet the winner of Tuesday's mouth-watering clash between Raducanu and the retiring Serena Williams.
American Sloane Stephens, the 2017 US Open winner, did not spend much time in the day's final match, taking down Alize Cornet 6-1 6-0. She will next meet world number one Iga Swiatek.
The main draw of the US Open starts on August 29th.
